Trademark Related Query & Domain name issue!

Hello Sir,

I would like to seek some information about trademark registration for a domain name of my client. Can you please help answer a few of my questions to clear up my queries.

1. Please note that for the sake of privacy, I am using fictitious domain names as per request from my client.

2. Suppose, the client is based in India and has a domain name as primedecor.com

3. The domain name is "primedecor.com" which is trademark registered in India. The site is called as "Prime Decor"

Case 1.

Now, if someone from another part of the world or US registers the same trademark in their country i.e. "Primedecor" or/and "Prime Decor", who would keep the domain in case of any dispute?

Does it also make a difference if the other party has registered the trademark for domain earlier/after than my client in US. (My client has already registered the trademark in India)

Case 2.

In case any entity registers domain name - "prime.com", and if that domain name "prime.com" & "Prime" are trademark registered in US.

Can "prime.com" take any objection to my clients domain "primedecor.com" which is called as "Prime Decor", now that the other party has a mark over the word "Prime".

Some General Questions:

1. Considering that the scope of the website is only to provide information to the internet surfers, is it necessary to register the trademark for this domain name worldwide or in US. Or is it alright to have it only in India.

2. What is the difference between domain name trademark and federal trademark?

3. If the US federal trademark doesn't apply, does a domain name trademark apply? If yes, what is the procedure to apply for it and from where should I apply?

4. In case, "primedecor.com" & "Prime Decor" is available for trademark registration worldwide, how do I go about registering it? Is it required to register it in every country or only registering at one central location would suffice.

Thank you very much and have a great day.

Regards,
SB